dorsal/arxiv
View SchemaLargest separable balls around the maximally mixed bipartite quantum state
| Authors | Leonid Gurvits, Howard Barnum |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0204159 |
| URL | https://arxiv.org/abs/quant-ph/0204159 |
| DOI | 10.1103/PhysRevA.66.062311 |
| Journal | Physical Review A, Vol. 66, Article no. 062311 (Dec. 2002) |
Abstract
For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of separable (unentangled) matrices around the identity matrix. This implies a simple and intutively meaningful geometrical sufficient condition for separability of bipartite density matrices: that their purity $\tr \rho^2$ not be too large. Theoretical and experimental applications of these results include algorithmic problems such as computing whether or not a state is entangled, and practical ones such as obtaining information about the existence or nature of entanglement in states reached by NMR quantum computation implementations or other experimental situations.
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"abstract": "For finite-dimensional bipartite quantum systems, we find the exact size of\nthe largest balls, in spectral $l_p$ norms for $1 \\le p \\le \\infty$, of\nseparable (unentangled) matrices around the identity matrix. This implies a\nsimple and intutively meaningful geometrical sufficient condition for\nseparability of bipartite density matrices: that their purity $\\tr \\rho^2$ not\nbe too large. Theoretical and experimental applications of these results\ninclude algorithmic problems such as computing whether or not a state is\nentangled, and practical ones such as obtaining information about the existence\nor nature of entanglement in states reached by NMR quantum computation\nimplementations or other experimental situations.",
"arxiv_id": "quant-ph/0204159",
"authors": [
"Leonid Gurvits",
"Howard Barnum"
],
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"quant-ph"
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"doi": "10.1103/PhysRevA.66.062311",
"journal_ref": "Physical Review A, Vol. 66, Article no. 062311 (Dec. 2002)",
"title": "Largest separable balls around the maximally mixed bipartite quantum state",
"url": "https://arxiv.org/abs/quant-ph/0204159"
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